Problem: What's the first wrong statement in the proof below that $ \triangle EFC \cong \triangle EBC$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle BAC \cong \angle CEF$ $, \ $ $ \overline{AC} \cong \overline{CE}$ $, \ $ $ \angle ACB \cong \angle ECF$ $, \ $ $ \overline{DE} \cong \overline{CE}$ $, \ $ $ \angle BDE \cong \angle ECF$ $, \ $ and $\ $ $ \angle DBE \cong \angle CFE$ Proof $ \triangle EFC \cong \triangle ABC$ because ASA $ \overline{CF} \cong \overline{BC}$ because corresponding parts of congruent triangles are congruent $ \angle CEF \cong \angle BCE$ because alternate interior angles are equal $ \overline{EF} \cong \overline{DF}$ because corresponding parts of congruent triangles are congruent $ \triangle EBD \cong \triangle EFC$ because AAS $ \triangle EFC \cong \triangle EBC$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{DF} \cong \overline{EF}$ is the first wrong statement.